Question

The following table shows a data set and the number of times each point is misclassified during a run of the perceptron algorithm (with offset θ0). θ and θ0 are initialized to zero.

i	x(i)	y(i)	times misclassified
1	[-4, 2]	+1	1
2	[-2, 1]	+1	0
3	[-1, -1]	-1	2
4	[2, 2]	-1	1
5	[1, -2]	-1	0

Write down the state of θ and θ0 after this run has completed (note, the algorithm may not yet have converged). Enter θ as a list [θ1,θ2] and θ0 as a single number;

θ = ?

θ0 = ?

Answer 1

θ=[0,0], θo=0

Here, for y=+1, θx+θo>0 and y=-1,θx+θo<=0

if x has label +1 but got misclasfied, then θ=θ+x

if x has label -1 but got misclassified, then θ=θ-x

Using perceptron algorithm,

θ=[-4,2]-2*[-1,-1]-[2,2] =[-4,2]

θo=1-2*1-1=-2

So,θ=[-4,2] and θo=-2